Sochi feels very far away. Western eyes are now fixed on Crimea, a Ukrainian peninsula about 500 miles west of the Olympic city, where local militias and politicians have mounted a separatist response to the Ukrainian revolution against Viktor Yanukovych's regime. Because Crimea is ethnically and politically complex, this move threatens the peace not only of Ukraine and Russia but also Crimea itself. Vladimir Putin has exacerbated this crisis. After a some sabre-rattling, we now hear reports of boots on the ground, even while Russia's official position remains murky. The new Ukrainian government decries an invasion; some observers fear a repetition of the 2008 war in Georgia; and western governments and Nato have warned Russia.

In the west there is talk of a return to the cold war, but this is wide of the mark: the sources of current Russian conduct lie in how different our world is to that of the Cold War, not how similar. Putin is not aggressive because he feels strong or unchallenged by a flabby west. Since the end of the Soviet Union, the EU and Nato have enlarged at the impressive clip of roughly one new member state every two years. Against this background, Putin has just suffered what he sees as a massive political defeat.

Putin was triumphant last November, when he seemed to have successfully (and shortsightedly) torpedoed the EU's association agreement with Ukraine. Now we see him frustrated for the second time in a decade by a country he fails to understand, afraid of "revolutionary contagion" and "domino" regimes. His plans for a "Eurasian" union lie in tatters, because without Ukraine, the rest will be a rump. All this is set against mounting problems in the Russian economy.

If the cold war taught us anything, it is that perceptions are crucial and empathy is not sympathy. One need not concede anything to know it is vital to understand Putin's motives. It is obvious he is wrong. Ukraine is a sovereign state: questioning its territorial integrity is unjustifiable and a danger to peace, domestic and international. But this doesn't matter to Putin, who is likely to genuinely sees himself as the aggrieved party, acting defensively. In reality he has only himself to blame – real Russian interest did not dictate his attack on an association agreement with the EU. But the Ukrainian revolutionaries' equally rash rejection of the Sikorski-Steinmeier-Fabius agreement – brokered by Poland, Germany and France – in which Yanukovych acceded to demands for a new coalition government and early elections, has given Putin a reason to feel that the west has acted in bad faith (again, whether he is right or wrong is beside the point).

Putin's macho image should not deceive us; neither should his statements lamenting the end of the Soviet Union (those keen to take his word for it should try to reconcile their literalism with their usual insistence that he is a deceitful scion of the KGB). The best analogy for him is not a post-1945 cold war warrior but a pre-1917 national imperialist. Quite plausibly, he would like to see himself as reviving Russia's greatness without actually relapsing into a cold war which, after all, he witnessed Russia lose. This makes Ukraine even more important for him because he perceives it not simply as part of the short-lived Soviet experiment, but of either Russia, or Russia's Huntingtonian zone of civilisational hegemony. That is wrong too, but the problem is Putin thinks he is right.

There are no simple solutions. Western warnings to Putin are necessary. But if they come without any face-saving offers, they will be worse than useless. Moreover, those urging the west to scare the imperialism out of Russia should also warn the new Ukrainian leadership that, while Crimea is indeed Ukrainian, restraint is urgently needed.

There is, after all, one more thing we can learn from the cold war. It was not peace: we got through it without one big hot war but with many nasty smaller ones, which devastated the societies in which they took place. Ukraine's territorial integrity, its chance to build a more democratic and equal society, and its free decision about the EU are all worth supporting; so is not having the country turn into a vicarious battlefield.